# Where is the “time and frequency” in a Discrete Wavelet Transform?

The DWT is motivated by the ability to see signal in time and frequency at the same time, if I understood that correctly.

I am using the following Matlab commands for some signal x:

[A,D] = dwt(x,'db4');


Then I plot A vs some vector t, representing 'time'. I do know the algorithm behind A and D: low (high) pass filter, then downsample by 2.

My questions: Where is the time axis and where is the frequency axis if I all what I have are the coefficients A (approximation) and D (detail)?

Second question: If all of this is a simple filtering and downsampling, I don't see what is new in DWT...

• The length of your vector of coeficient should be $\frac{N}{2}$ which is the downsampled and filtered original signal. And indeed you may call that "one level of frequency". in fact, this is not really one level of frequency : this is the output of a filter, so the frequency information you get depends on your filter's frequency response. For instance if the low pass filter allow everything below 50hz to pass without attenuation and eveything above is perfectly blocked, the output coeficients are the 0-50hz component of your original signal. – Antoine Bassoul Apr 24 '15 at 18:29